The Denkiri Arm was a spiral extension of the Milky Way Galaxy located in the Gamma Quadrant, at a distance from the Federation which would have taken nearly a century at warp nine to cover.
In 2366, a wormhole was discovered near the planet Barzan II which led to an area beyond the Denkiri Arm. At the time, it was thought to be the first stable wormhole ever discovered, but it was eventually found that the Gamma Quadrant terminus periodically shifted positions, making it untenable to interstellar travel. (TNG: "The Price")
According to Rick Sternbach, the arm was named after a species he came up with for a non-Trek story he wrote. Two paintings he created of planets in their home system, as well as an Phylogenetic tree for life at Denkir IV, made it on screen as set decorations. More info on the story can be found here.
